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It is a well known fact, that the disorder has its most dramatic effects onthe conventional quantum transport in one dimensional systems. In flat band(FB) systems, it is revealed that the conductivity at the FB energy is robustagainst the disorder and can even be tremendously boosted. Furthermore,challenging our understanding of the physical phenomena, the giant increaseoccurs in the limit of low FB states density. The singular behaviour of thequantum metric of the FB eigenstates is found to be at the heart of theseunexpected and puzzling features. Our findings should have interesting falloutfor other physical systems, and may as well open up engineering strategies toboost the critical temperature in two dimensional superconducting FB materials.

Giant boost of the quantum metric in disordered one dimensional flat band systems